Factorizations of Primitive Permutation Groups
نویسنده
چکیده
منابع مشابه
Unitary Matrix Integrals, Primitive Factorizations, and Jucys-Murphy Elements
A factorization of a permutation into transpositions is called “primitive” if its factors are weakly ordered. We discuss the problem of enumerating primitive factorizations of permutations, and its place in the hierarchy of previously studied factorization problems. Several formulas enumerating minimal primitive and possibly non-minimal primitive factorizations are presented, and interesting co...
متن کاملBivariate Factorizations Connecting Dickson Polynomials and Galois Theory
In his Ph.D. Thesis of 1897, Dickson introduced certain permutation polynomials whose Galois groups are essentially the dihedral groups. These are now called Dickson polynomials of the first kind, to distinguish them from their variations introduced by Schur in 1923, which are now called Dickson polynomials of the second kind. In the last few decades there have been extensive investigations of ...
متن کاملOn Orbital Partitions and Exceptionality of Primitive Permutation Groups
Let G and X be transitive permutation groups on a set Ω such that G is a normal subgroup of X. The overgroup X induces a natural action on the set Orbl(G,Ω) of non-trivial orbitals of G on Ω. In the study of Galois groups of exceptional covers of curves, one is led to characterizing the triples (G,X,Ω) where X fixes no elements of Orbl(G,Ω); such triples are called exceptional. In the study of ...
متن کاملThe Minimal Base Size of Primitive Solvable Permutation Groups
A base of a permutation group G is a sequence B of points from the permutation domain such that only the identity of G fixes B pointwise. Answering a question of Pyber, we prove that all primitive solvable permutation groups have a base of size at most four.
متن کاملOn the Relational Complexity of a Finite Permutation Group
The relational complexity ρ(X,G) of a finite permutation group is the least k for which the group can be viewed as an automorphism group acting naturally on a homogeneous relational system whose relations are k-ary (an explicit permutation group theoretic version of this definition is also given). In the context of primitive permutation groups, the natural questions are (a) rough estimates, or ...
متن کامل